LPRS Analysis of Singularly Perturbed Sliding Mode Control Systems

• 成果类型: Article
• 署名作者: Aljaberi, Saeed M.; Boiko, Igor
• 署名单位: Technology Innovation Institute; Khalifa University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3392031
• 发表日期: 2024
• 页码: 7081-7087
• 关键词: Relays; oscillators; Perturbation methods; Power system dynamics; aerodynamics; actuators; Robot sensing systems; chattering; discontinuous control; Frequency-domain analysis

摘要

In this article, we examine singularly perturbed sliding mode (SPSM) control systems with linear plants using the Locus of a Perturbed Relay System (LPRS) method. We derive necessary conditions for the existence of chattering, which depend on both the singular perturbation parameter and the plant dynamics. Moreover, concerning the singular perturbation parameter and plant dynamics, we demonstrate that the model of the averaged or slow motions in an SPSM system is of reduced order if an ideal sliding mode takes place and nonreduced if chattering occurs. Finally, starting from the definition of the LPRS, we derive first-order approximations of the chattering frequency and period, as well as the equivalent gain of the relay. The results are illustrated and applied on first- and second-order systems, as well as an example of a dc motor connected to a dynamic sensor.